This paper investigates the effects of localized interface progressive delamination on the behavior of two-layer laminated composite plates when subjected to low velocity impact loading for various fiber orientations. By means of finite element approach, the laminae stiffnesses are constructed independently from their interface, where a well-defined virtually zero-thickness interface element is discreetly adopted for delamination simulation. The present model has the advantage of simulating a localized interfacial condition at arbitrary locations, for various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. In comparison, the model shows good agreement with existing results from the literature when modeled in a perfectly bonded state. It is found that as the local delamination area increases, so does the magnitude of the maximum displacement history. Also, as top and bottom fiber orientations deviation increases, both central deflection and energy absorption increase although the relative maximum displacement correspondingly decreases when in contrast to the laminates perfectly bonded state.

Interfacial imperfection that eventually leads to the delamination of laminated composite plates is commonly considered as one of the chief contributors to performance degradation of these advanced lightweight materials. This imperfection is structurally harmful and contributes principally to the failure of the laminate especially in presence of dynamic loading environment such as impact loading. The imperfection in the interface may be due to insufficient adhesion or incorrect equipment setting during manufacturing, leading it to undergo serious damage such as matrix cracks, fibers breakages, or delamination. These kinds of damage are severe because they drastically reduce the mechanical characteristics of the laminate and at the same time can leave visible marks on the impacted surface. Therefore, understanding the interface condition effect on laminated composite plates is of great importance for improvement of the plate’s strength.

In terms of loading environment, laminated composite plates are prone to impact loads that occur during manufacturing, transportation, or service life. These impact loads are considered extremely dangerous and cause invisible damage to the back face or within the laminate which consequently reduce the strength of the composite material, even when the impact produces low energy. It has been proven that if a composite plate is subjected to a low velocity impact, the damaged area will increase with the increase of the impact velocity [

In general, there exist several factors that significantly influence the behavior of composite materials when subjected to impact loading. They can basically be divided into two parts. The first part involves the laminate properties such as shape, size, thickness, ply orientation, and stacking sequence. The second category corresponds to impactor properties such as impactor shape, velocity, and energy.

In regard to the thickness effect of the composite, an extensive study on thin and standard CFRP laminates was performed by Shi et al. [

Tiberkak et al. [

Many researches have been conducted regarding how the fiber orientation influences the impact behavior of laminated composites. The effect of laminate reinforcement arrangement on the behavior of polymer matrix composites was studied using a simply supported plate with dimensions of 150 mm × 150 mm × 6 mm [

The low velocity impact of E-glass/epoxy laminated composite plates using three rectangular plates of 150 mm × 50 mm, 150 mm × 100 mm, and 150 mm × 150 mm dimensions was studied by Aslan et al. [

The effects of high velocity impacts (ballistic impact) on carbon/epoxy composite panels using hemispherical, conical, fragment simulating, and flat impactors were studied by Ulven et al. [

In connection with the interfacial degeneration behaviors, early works on the imperfect bonding had been focused on the shear slip in cross-ply laminates adopting Pagano’s analytical solutions [

Although numerous studies were devoted to impact behavior of composite plates, it should be noted that there exists little literature evidence on the effects of delaminated interface in particular that exists locally. The current paper aims to fill this gap by focusing on the behavior of two-layer laminates subjected to low velocity impact. The paper is arranged as follows. After the introduction, we present the finite element modeling procedure for a two-layer composite plate, consisting of two laminae with a well-defined virtually zero-thickness interface element in between. The effects of locally delaminated laminates which vary in area from the center outwards are then discussed in the presence of impact loading. In the end, we conclude the main findings of our study.

Figure

(a) Configuration of composite laminate. (b) DOF of lamina subelements and an interface element that lies in between.

The governing equation of this study can be formulated as follows:

The stiffness of the laminate is computed by adding up the stiffness of each subelement in all layers in the laminate including the interface layer. The elemental stiffness matrix is computed by relating the

In terms of the FEM description, each lamina is modeled by a four-node lamina subelement. The corresponding arrangements of nodes and degrees of freedom (DOF) are shown in Figure

The stiffness matrices of the lamina subelements are assembled in the local stiffness matrix of the laminate element as follows:

For this study, we adopt here for the interface layer a virtually zero-thickness interface element. There are eight nodes in the zero-thickness interface element, the node sequence of which is arranged in anticlockwise manner from bottom to top as shown in Figure

It should be noted that the shape function of the zero-thickness interface element in this study is a 2-dimensional Lagrange shape function rather than that of a 3-dimensional one although the interface element resembles the geometrical configuration of a solid element. Since the interface in this study is considered an orthotropic material with zero normal stresses in

In the present study,

In this study, we only study the localized imperfection with a uniform degeneration in

For the mass matrix of the laminated composite plate, the consistent mass matrix is employed. The mass matrix

The element mass submatrices are given as follows:

Newmark’s numerical time integration method is employed to calculate the time-dependent impact loading, which is applied to the plate. Newmark’s integration scheme starts by assuming initial force

The velocities and accelerations can also be computed by first computing the effective stiffness matrix:

Solving for displacement at time

Thus, the accelerations and velocities are computed as, respectively,

The time step chosen for this study is 1.4 ms following the study of Shi et al. [

Plate’s properties and dimensions.

Length and width of plate | 100 mm × 100 mm |

Stacking sequence | Upper lamina (0°) and |

Thickness of plate | 0.5 mm |

Material properties |
^{3}, and |

Table

Natural frequencies of the first eight mode shapes.

Mode sequence number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Shi et al. (2004) [ |
23.249 | 38.825 | 55.37 | 59.814 | 72.984 | 85.337 | 101.53 | 104.6 |

Present study | 23 | 37 | 53 | 58 | 77 | 84 | 96 | 103 |

Difference, % | 1.1 | 4.7 | 4.28 | 3 | 5.21 | 1.56 | 5.45 | 1.53 |

Figure

Displacement history of laminate with

Displacement history of laminate with

For the laminate with

Displacement history of laminate with

From Figures

Define the displacement ratio at any given time as follows:

Relationship between area ratio and maximum displacement ratio for (a)

The delamination energy of each case can be established by calculating the area under the force-displacement curve, for each delamination case starting from

Force-displacement relationship of laminates with (a)

It is evident that an increase in the top-bottom angle deviation leads to an increase in the absorbed energy. That means as

The paper presents finite element formation of a two-layer composite plate with localized interfacial delamination in the presence of impact load employing a well-defined virtually zero-thickness interface element. The following conclusions are obtained.

As the area of delamination increases, the central displacement increases indicating that it is directly proportional to the area of delamination.

Whenever the top fiber orientation

As

The increase in

The authors declare that there is no conflict of interests regarding the publication of this paper. This research is not influenced by a secondary interest, such as financial gain or anything else.

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.